Editing Structured program theorem (section)

=== Single-while-loop, folk version of the theorem ===
This version of the theorem replaces all the original program's control flow with a single global <code>while</code> loop that simulates a [[program counter]] going over all possible labels (flowchart boxes) in the original non-structured program. Harel traced the origin of this folk theorem to two papers marking the beginning of computing. One is the 1946 description of the [[von Neumann architecture]], which explains how a [[program counter]] operates in terms of a while loop. Harel notes that the single loop used by the folk version of the structured programming theorem basically just provides [[operational semantics]] for the execution of a flowchart on a von Neumann computer.<ref name="Harel"/>{{rp|383}} Another, even older source that Harel traced the folk version of the theorem is [[Stephen Kleene]]'s [[Kleene's T predicate|normal form theorem]] from 1936.<ref name="Harel"/>{{rp|383}}

[[Donald Knuth]] criticized this form of the proof, which results in [[pseudocode]] like the one below, by pointing out that the structure of the original program is completely lost in this transformation.<ref>{{cite journal
 |  author = Donald Knuth
 |   title = Structured Programming with go to Statements
 | journal = Computing Surveys
 |  volume = 6
 |   issue = 4
 |    year = 1974
 |   pages = 261–301
 |   doi = 10.1145/356635.356640
|   citeseerx = 10.1.1.103.6084
 | s2cid = 207630080
 }}</ref>{{rp|274}} Similarly, Bruce Ian Mills wrote about this approach that "The spirit of block structure is a style, not a language. By simulating a Von Neumann machine, we can produce the behavior of any spaghetti code within the confines of a block-structured language. This does not prevent it from being spaghetti."<ref name="Mills2005">{{cite book|author=Bruce Ian Mills|title=Theoretical Introduction to Programming|year=2005|publisher=Springer|isbn=978-1-84628-263-8|page=279}}</ref>

<syntaxhighlight lang="pascal">
p := 1
while p > 0 do
    if p = 1 then
        perform step 1 from the flowchart
        p := resulting successor step number of step 1 from the flowchart (0 if no successor)
    end if
    if p = 2 then
        perform step 2 from the flowchart
        p := resulting successor step number of step 2 from the flowchart (0 if no successor)
    end if
    ...
    if p = n then
        perform step n from the flowchart
        p := resulting successor step number of step n from the flowchart (0 if no successor)
    end if
end while
</syntaxhighlight>